English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In [22], the second author showed that given a holomorphic quadratic differential on the unit disk of the complex plane C, one can construct a harmonic diffeomorphism from the hyperbolic two space H into itself so that its Hopf differential is equal to the given one. Later, in [4], Au and the second author generalized the result for holomorphic quadratic differentials on C, provided the differential is not of the form cdz for some constant c. Even though it is not explicitly stated in [22, 4], the harmonic diffeomorphism is unique up to an isometry in the target. The method of proof in [22, 4] is to construct a complete constant mean curvature space-like surface (a constant mean curvature cut) in the Minkowski three space from the given holomorphic quadratic differential. The required harmonic diffeomorphism is just the Gauss map of the constant mean curvature cut. On the other hand, Li, Wang and the first author [17] studied a class of surfaces which is more general than the hyperbolic two space. They studied complete simply connected surfaces with Gaussian curvatures bounded between a negative constant and 0, so that the first eigenvalue for the Laplacian for functions is positive. Following [17], we call such a surface a hyperbolic Cartan-Hadamard surface, or simply a hyperbolic CH surface. For example, a simply connected surface with Gaussian curvature pinched between two negative constants is a hyperbolic CH surface. It was proved in [17] that a

Harmonic diffeomorphisms into Cartan–Hadamard surfaces with prescribed Hopf differentials